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Ruthlessbaby · 2021年03月31日

没有给出借谁投谁

NO.PZ2019103001000061

问题如下:

Susan Winslow manages bond funds denominated in US Dollars, Euros, and British Pounds. Each fund invests in sovereign bonds and related derivatives. Each fund can invest a portion of its assets outside its base currency market with or without hedging the currency exposure, but to date Winslow has not utilized this capacity. She believes she can also hedge bonds into currencies other than a portfolio’s base currency when she expects doing so will add value. However, the legal department has not yet confirmed this interpretation. If the lawyers disagree, Winslow will be limited to either unhedged positions or hedging into each portfolio’s base currency.

Winslow thinks the Mexican and Greek markets may offer attractive opportunities to enhance returns. Yields in these markets are given in Exhibit 1, along with those for the base currencies of her portfolios. The Greek rates are for euro-denominated government bonds priced at par. In the other markets, the yields apply to par sovereign bonds as well as to the fixed side of swaps versus six-month Libor (i.e., swap spreads are zero in each market). The six-month Libor rates also represent the rates at which investors can borrow or lend in each currency. Winslow observes that the five-year Treasury-note and the five-year German government note are the cheapest to deliver against their respective futures contracts expiring in six months.

Winslow expects yields in the US, Euro, UK, and Greek markets to remain stable over the next six months. She expects Mexican yields to decline to 7.0% at all maturities. Meanwhile, she projects that the Mexican Peso will depreciate by 2% against the Euro, the US Dollar will depreciate by 1% against the Euro, and the British Pound will remain stable versus the Euro. Winslow believes bonds of the same maturity may be viewed as having the same duration for purposes of identifying the most attractive positions.

Based on these views, Winslow is considering three types of trades. First, she is looking at carry trades, with or without taking currency exposure, among her three base currency markets. Each such trade will involve extending duration (e.g., lend long/borrow short) in no more than one market. Second, assuming the legal department confirms her interpretation of permissible currency hedging, she wants to identify the most attractive five-year bond and currency exposure for each of her three portfolios from among the five markets shown in Exhibit 1. Third, she wants to identify the most attractive five-year bond and hedging decision for each portfolio if she is only allowed to hedge into the portfolio’s base currency.

Among the carry trades available in the US, Euro, and UK markets, the highest expected return for the USD-denominated portfolio over the next 6 months is closest to:

选项:

A.

0.275%

B.

0.85%

C.

0.90%.

解释:

B is correct.

The highest potential return, 0.85%, reflects borrowing USD for 6 months and buying the UK 5-year bond. The carry component of the expected return is actually a loss of 0.15% [= (1.10% – 1.40%)/2], but this is more than offset by the 1% expected appreciation of GBP versus USD. A much higher carry component +0.90% = (1.95% – 0.15%)/2 could be obtained by borrowing for 6 months in EUR to buy the US 5-year note, but that advantage would be more than offset by the expected 1% loss from depreciation of the USD (long) against the Euro (short).

A is incorrect because a higher expected return of 0.85% can be obtained. This answer, +0.275% [= (1.95% – 1.40%)/2], is the highest carry available over the next 6 months within the US market itself (an intra-market carry trade).

C is incorrect. This answer (+0.90%) is the highest potential carry component of return but ignores the impact of currency exposure (being long the depreciating USD and short the appreciating Euro).

因为,inter-market carry trade 本身就是不 hedge,在答案没有给出借谁投谁的情况下,不能直接说借低利率投高利率就是最大策略收益(实际上只有intra-marker才能直接这样判定)。而是要综合汇率变化率对吗?本题答案没有给出借谁投谁的情况下,我们实际上是要每种借法投法都要计算一下综合收益,才能得出结论
1 个答案

发亮_品职助教 · 2021年04月02日

嗨,从没放弃的小努力你好:


因为,inter-market carry trade 本身就是不 hedge,在答案没有给出借谁投谁的情况下,不能直接说借低利率投高利率就是最大策略收益(实际上只有intra-marker才能直接这样判定)。而是要综合汇率变化率对吗?


正确。

Inter-market carry trade的收益来自两个部分,第一个部分是息差,第二个部分是汇率变动。两者加总才是Carry trade的总收益。


本题答案没有给出借谁投谁的情况下,我们实际上是要每种借法投法都要计算一下综合收益,才能得出结论


正确。理论上要全部算一遍才能有保证。不过像这道题给出了答案,咱们可以倒推着判断,这是一个思路。


不过这里还是有一个简便方法,另外一个思路,Carry trade的收益就来自息差和汇率波动,这两部分;


我们就先找汇率收益最大的一组,这样就直接可以定位到做Carry trade的两个货币,例如,在USD/GBP/EUR三种货币中,USD相对EUR、GBP贬值1%;那仅仅从汇率的角度出发,合适的Carry trade一定是投资EUR(Or GBP)利率,借钱的利率一定是USD;

即,方式1:借USD、投EUR

方式2:借USD、投GBP


因为USD相对贬值1%,最终了结Carry trade时,把EUR(Or GBP)的投资换成USD,会赚取1%的汇率收益。我们从汇率收益最高的角度出发,直接定位到了Carry trade最优的备选货币Pairs。


然后我们就看了,具体是方式1的息差高,还是方式2的息差高。

方式1,借USD投EUR,最大息差为:(0.6%-1.40%)/2

方式2,借USD,投GBP的最大息差为:(1.10%-1.40%)/2

显然,最优的Carry trade为,借USD、投GBP,总收益为:(1.10%-1.40%)/2 + 1% = 0.85%


以上是先找汇率收益最大的货币Pairs,然后再确定合适的利率期限,最终可以算出来Carry trade的收益为0.85%;0.85%是一个备选最优的Carry trade.


接下来就从息差入手,我们先找息差最大的一组Carry trade,在UK,US,EUR市场中,显然是借EUR投US息差收益最高,为:

(1.95%-0.15%)/2 = 0.9%

由于借EUR投USD,最终需要把USD的收益换回EUR,汇率损失-1%,所以整个策略的净收益为:

0.9% - 1% = -0.10%


显然,本题可以判断出来是借USD、投GBP的收益最高。


以上是一种快捷办法,总结下:


反正收益是来自①息差收益,②汇率波动;


我们就分别先找到汇率收益最大的一组货币Pair、确定借贷的货币之后,然后再找合适的利率期限,这是一个备选Carry trade;


第二个备选策略,我们找息差最大的一组货币Pair,然后再考虑到汇率波动,可以算出来这一个备选Carry trade的净收益;

这两个备选Carry trade进行PK,收益最大的就是最优的Carry trade。

以上方式,基本上可以快捷定位到最优的Carry trade。

----------------------------------------------
努力的时光都是限量版,加油!

Ruthlessbaby · 2021年04月02日

发亮大神可以加我微信吗?膜拜你很久了

发亮_品职助教 · 2021年04月02日

谢谢~谢谢~ 可以在班级群里找下帅帅老师,或者在企业微信里呼一下~

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